Speical Systems Theory is a Mathematical Systems Theory concerning the necessary conditions for the possibility of anomalous phenomena like Life, Consciousness and Sociality which exist but are unexplained inadequately by contemporary scientific theory

The idea of Special Systems Theory is to set the mathematically necessary conditions for the possibility of life, consciousness and the social, three very special anomalous phenomena. The necessary conditions are set by Mathematics which structure the possibility space in which anomalous emergent processes can occur as we see in Life, Consciousness, and Sociality which we have in ourselves and other life forms existential proof of their existence even though they cannot be explained by standard theories of Science yet. The whole idea of the meta-theory is to set the external limiting conditions that mathematics gives for understanding the phenomena. And those external conditions are in the form of mathematical anomalies that make ultra-efficacious phenomena like Life, Consciousness and Sociality possible. The bridge between the existential proof which we are as living conscious social beings and the mathematical possibility based on anomalous structures in mathematics is the meta-theory Special Systems Theory itself that is part of Systems Science and an addition to General Systems Theories within Systems Science. The relation between Systems and Special Systems are explained by Schemas Theory (http://schematheory.net).

I take mathematical anomalies of different sorts that have basically the same structure and build a meta-theory that has a radically different structure than normal general systems theories. Then within the meta-theory are placed local theories that explain the phenomena of life, consciousness and the social very much along the lines of what Terrance Deacon has envisaged in Incomplete Nature, but he has not mathematics to back up his claims and he leaves out the social layer of emergence and only deals with life and consciousness. He however does the service of re-explaining basic scientific concepts in a way that makes Life and Consciousness plausible rather than the normal explanations that would render these phenomena improbable or impossible.

The concept is to use anomalies in mathematics as the basis for explaining the possible existence of anomalies in the physical world that would give us emergent features like life, consciousness, and the social. The meta-theory specifies the emergent differences between these phenomena and some of their very general properties. Then more specific theories related to each phenomena are substituted into the meta-theory to explain the phenomena in more detail in this case Prigogine’s theory of Dissipative Structures augmented by the Construal Flow theory of Bejan, a modified form of the existential theory of life of Maturana and Varella called Autopoiesis, and Reflexive Sociology to explain the social in more detail. We take the meta-theory as being fixed by mathematical anomalies that are related to each other by their general structure to specify the Special Systems Theory, then we allow the contained theories to be modified to better and better explain the link between the mathematics and the anomalous phenomena in question, be it life, consciousness or the social. The meta-theory explains the interaction between the Special Systems based on the structure of Hyper-complex algebras and other types of mathematics or some anomalous physical theories like the theory of Solitons, Breathers, and Instantatons, or Cooper pairs in super-conductivity or Bose-Einstein condensates. Thus there is a physical component to the theory based on specific physical phenomena that have the same structure as the mathematical anomalies.

Special Systems Theory has been constructed so that it as to be refutable by using different anomalies in mathematics to structure the special systems in order to give a very specific theoretical structure to the explanation offered. Unless we make our systems theories refutable there is no way to make progress. Special Systems Theory is meant to be an example of what a good theory of the phenomena might look like rather than the final answer. A good theory would be based in mathematics and testable, thus refutable.

Special Systems Theory was discovered through an analysis of the imaginary cities of Plato and then relating the anomalous structures of those cities to Anomalies in Mathematics. It was realized that these anomalous structures in mathematics which were all similar could be used to produce a general Systems Theory about these Special Systems. Then it was realized that Special Systems Theory could be used to set the limits of the necessary conditions of the possibility of anomalous phenomena like Life, Consciousness and the Social. The combination of mathematical anomalies and physical anomalies with the same basic structure makes it possible to explain things that normal Systems Theory cannot explain and thus its value in Systems Science and for other special sciences that need to explain anomalous phenomena with similar structures.